zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On semilinear problems with nonlinearities depending only on derivatives. (English) Zbl 0852.34018
The authors consider semilinear boundary value problems $$u''(t)+ \lambda_1 u(t)+ g(t, u'(t))= f(t),\quad t\in I,\tag1$$ $$(Bu)(t)= 0,\quad t\in \partial I,\tag2$$ where $I= [0, \pi]$, $B$ denotes either the Dirichlet or the Neumann or the periodic boundary conditions, respectively, and $\lambda_1$ is the first eigenvalue of the corresponding linear problem $u''(t)+ \lambda u(t)= 0$, $t\in I$, $(Bu)(t)= 0$, $t\in \partial I$. The nonlinear function $g$ is supposed to be bounded and, in some cases, satisfies additional differentiability assumptions and asymptotic conditions. The authors emphasize the dependence of $g$ on the derivative of the solution $u'(t)$ in order to show the qualitative difference of this case and the Landesman-Lazer-type problem in which the nonlinearity $g$ depends only on the solution $u(t)$. The authors establish the solvability of the problem (1), (2).

34B15Nonlinear boundary value problems for ODE
34C25Periodic solutions of ODE
Full Text: DOI